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If a character is deranged, or has just lost it for a moment, one eye is drawn as being very different than the other. Commonly, the Mad Eye (or its iris/pupil) is much larger than the other. Can also double as an unspoken Oh, Crap moment. For extra effect, may be paired with Twitchy Eye.
Protagonist Kaneki Ken has one, as a result of being a Half-Human Hybrid. His right eye remains normal, but his left is prone to giving awayhis Ghoul nature. He frequently wears an eye-patch to conceal it. (It turns out to be a tell-tale sign of any Half-Human Hybrid, known as One-Eyed Ghouls.)
Kureo Mado, a sadist CCG Investigator obsessed with killing Ghouls to produce new anti-Ghoul weapons, has one lazy eye and one that is almost always bulging.
Falling under the "Deranged Character" subset are The Joker's eyes as drawn in Batman: RIP. There, one of his pupils is drawn slightly larger than the other, giving him a dangerous and mentally off-kilter look. The effect is so slight that it's only noticeable in close-up shots of the character, but it's definitely there. Then again, he is a Monster Clown with enough crazy to fill Arkham Asylum's halls ten times over.
Most Returners in Dead Eyes Open seem to have one eye permanently open with a shrunken pupil.
In 9, 6 has one eye slightly larger than the other as a permanent feature, confirming his Cloudcuckoolander status.
In An American Tail: Fievel Goes West, Wiley Burp teaches Tiger how to intimidate someone using "The Laaaayyyyzzzzyyy Eyyyyye!" which is essentially an intentional ecovation of this trope.
Films — Live-Action
In The New Guy, Luther teaches Dizzy his "Crazy Eye" which consists of squinting one eye and opening the other wide.
The aptly-named Mad-Eye Moody from Harry Potter has a magical replacement eye. It's bright blue, the size of a golf-ball, has 360 rotation and can see through just about anything. It's also virtually never looking in the same direction as his other eye.
The unnamed old man in Edgar Allan Poe's classic The Tell-Tale Heart. One eye, due to some deformity, is described as a "vulture eye" with a film over it. However, the eye drives the old man's roommate to insanity (whether this roommate is his servant, his apprentice, a caretaker or even his spouse is never mentioned).
Scorpion Shards: Everyone maddened by Dillon gets one dilated pupil and one pinpoint pupil
Live Action TV
Doctor Who: The Fourth Doctor's eyes do not quite ever point in the same direction, which is a really big part of how mad he looks. (The actor is perfectly capable of pointing both his eyes in the same direction when not in character.) His pupils are also noticeably off-centre.
Having a literal Mad Eye is Older Than Print: Cuchulain, the Irish folk hero. Whenever he went into one of his unstoppable rages, one of his eyes would get smaller and the other would get bigger. " ... he sucked one eye so deep into his head that a wild crane couldn't probe it onto his cheek out of the depths of his skull; the other eye fell out along his cheek." Now thats a Mad Eye.
Crazy Dave from Plants vs. Zombies. He's craaaaaazy. All the zombies in the game also have larger left eyes.
For some reason, Liara in the Mass Effect series is often shown with one eye squinting slightly more than the other, prompting many a joke along this line.
Black Mage, from 8-Bit Theater does this a lot, and was stuck for a while after a particular bit of frustration. As he put it after listening to one of Red Mage's "plans", "That's so stupid I can't even see straight."
The titular amorph from Schlock Mercenary has one eye that is literally larger than the other, and the cartoonist is consistent about which is which, and what side each is on. Since Schlock can move his eyes around it doesn't really matter though.
Several characters in Girl Genius do this sometimes... and there's one, a construct, who really does have one eye bigger than the other.
Bob from Bob the Angry Flower. When Bob's scorching feral mania comes to the fore, he gets the Mad Eye.
Vatsy, the insane journalist from Vatsy And Bruno, is always drawn with one eye in shadow to accentuate his wrong-ness.
The Tick — the title character, who is never entirely straight.
Vince from Rex The Runt, one of the more random oddballs in claymation: given to random fits of Pavarotti and tangential one-word sentences.
The starring spider in the (still unfinished) Art Institute of Portland student production Tangled Web, sometimes. Then again, he's decided to become a vegetarian and is desperate to avoid the delicious, delicious fly that's just landed in his web, so can you really blame him?
The Vigar puppet on BRATS Of The Lost Nebula was the first one with different sized eyes to be approved by Brian Henson.
VERY evident on Ed, Edd n Eddy. "Boy Double D. Eddy never stares at ME like that."
In The Critic, Duke Phillips once answered a reporter's question by telling him to "stare deep into the hypnotic powers of my EEEeeevil eeeye!" It apparently works.
Two-Face gets this treatment as an effect of stylization in Batman: The Animated Series, as does Jonah Hex in the episode "Showdown." Characters that aren't completely human, such as Man-Bat and Clayface, sometimes do this.
Dr. Mystico on Freakazoid!, as if his introductory speech weren't enough of a giveaway.
Anisocoria, or asymmetric pupil dilation, can be a sign of serious neurological problems. This is also one of the first things EMTs check for when they suspect a concussion.